Bring 4-5 quarts of water to a boil in a large saucepan or pot . Add ¼ cup salt.
Prep the broccolini: Trim off the very bottom of the broccolini stems (about ½-inch). Slice off the florets. Halve any florets that are bigger than 3 inches wide. Slice the stalks into approximately 1 ½-2-inch pieces.
Drop the broccolini into the boiling water and cook 2 minutes. Drain immediately, then transfer to a serving bowl.
Pour the olive oil over the broccolini and toss gently with tongs. Squeeze the lemon wedges over. Serve warm or at room temperature.
To make ahead, cook, drain and immediately rinse under cold running water to preserve the color. Drain again and drizzle with olive oil. Store refrigerated up to 5 days.
When ready to cook, sauté the broccolini for a minute or two in olive oil.
Want to roast broccolini? After tossing with olive oil spread out on a sheet pan and roast at 450 degrees or under the broiler until the edges are slightly charred.